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The capacity constrained facility location problem

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  • Aziz, Haris
  • Chan, Hau
  • Lee, Barton E.
  • Parkes, David C.

Abstract

We initiate the study of the capacity constrained facility location problem from a mechanism design perspective. In the capacity constrained setting, the facility can serve only a subset of the population, assumed to be the k-closest with respect to agents' true locations (this can be justified as the essentially unique equilibrium outcome of a first-come-first game induced by the facility location). The main result is a complete characterization of dominant-strategy incentive compatible (DIC) mechanisms via the family of generalized median mechanisms (GMMs). Thus, the framework we introduce surprisingly provides a new characterization of GMMs, and is responsive to gaps in the current social choice literature highlighted by Border and Jordan (1983) and Barberà et al. (1998). We also provide algorithmic results and study the performance of DIC mechanisms in optimizing welfare. Adopting a worst-case approximation measure, we attain tight lower bounds on the approximation ratio of any DIC mechanism.

Suggested Citation

  • Aziz, Haris & Chan, Hau & Lee, Barton E. & Parkes, David C., 2020. "The capacity constrained facility location problem," Games and Economic Behavior, Elsevier, vol. 124(C), pages 478-490.
    • Handle: RePEc:eee:gamebe:v:124:y:2020:i:c:p:478-490
    DOI: 10.1016/j.geb.2020.09.001
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    1. Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
    2. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
    3. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    4. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    5. Margaret L. Brandeau & Samuel S. Chiu, 1989. "An Overview of Representative Problems in Location Research," Management Science, INFORMS, vol. 35(6), pages 645-674, June.
    6. Jackson, M.O.Matthew O. & Nicolo, Antonio, 2004. "The strategy-proof provision of public goods under congestion and crowding preferences," Journal of Economic Theory, Elsevier, vol. 115(2), pages 278-308, April.
    7. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    8. T. Storcken & H. Peters & H. v. d. Stel & W. Peremans, 1997. "Strategy-proofness on Euclidean spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(3), pages 379-401.
    9. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
    10. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    11. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    12. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    13. Ehlers, Lars, 2002. "Multiple public goods and lexicographic preferences: replacement principle," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 1-15, February.
    14. Eun Heo, 2013. "Strategy-proof rules for two public goods: double median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 895-922, October.
    15. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    16. Nehring, Klaus & Puppe, Clemens, 2007. "Efficient and strategy-proof voting rules: A characterization," Games and Economic Behavior, Elsevier, vol. 59(1), pages 132-153, April.
    17. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    18. Anna Bogomolnaia & Antonio Nicolò, 2005. "Stable Assignment of Public Facilities under Congestion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(1), pages 65-91, February.
    19. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 491-514, June.
    20. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    21. Eiichi Miyagawa, 2001. "Locating libraries on a street," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 527-541.
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    Cited by:

    1. Qi Zhao & Wenjing Liu & Qingqin Nong & Qizhi Fang, 2023. "Constrained heterogeneous facility location games with max-variant cost," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-20, April.
    2. Yingyi Huang & Xinyu Wang & Hongyan Chen, 2022. "Location Selection for Regional Logistics Center Based on Particle Swarm Optimization," Sustainability, MDPI, vol. 14(24), pages 1-10, December.
    3. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    4. Andrew Jennings & Rida Laraki & Clemens Puppe & Estelle Varloot, 2021. "New Characterizations of Strategy-Proofness under Single-Peakedness," Papers 2102.11686, arXiv.org, revised Jun 2022.

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